If `P_1:vec r.vecn_1-d_1=0` `P_2:vec r.vec n_2-d_2=0` and `P_3:vec r.vecn_3-d_3=0` are three non-coplanar vectors, then three lines `P_1= 0`, `P_2=0`; `P_2=0`,`P_3=0` ; `P_3=0` `P_1=0` are

Options

A. parallel lines
B. coplanar lines
C. coincident lines
D. concurrent lines

Answer

d

Explanation

`P_(1)=P_(2)=0 ,P_(2)=P_(3)=0andP_(3)=P_(1)=0` are lines of intersection of the three plane `P_(1)=P_(2)andP_(3)`.
As `vecn_(1),vecn_(2)andvecn_(3)` are non-coplanar, plane `P_(1),P_(2)andP_(3)` will intersect at unique point. So the given lines will pass through a fixed point.